Mathematics as the only language is not enough

Economists barely communicate in natural language anymore. Thus, economics cannot do justice to relevant question of society, according to Michael Roos who advocates a change to the underlying ideology.

Mathematics has become the dominant language in economics. In the eyes of many economists, this is what makes the discipline a true science and renders it superior to other social sciences.

Framing theories of social science in mathematical terms has many advantages, no doubt. I do not dismiss it outright. However, it does narrow down the way of thinking. Economists do not address certain economic problems, at least not to a sufficient extent, because those problems cannot be mathematised. Mathematical methods are useful because they enforce precision and render arguments transparent and comprehensible. We can use them to prove the logical correctness of an argument. This is because mathematics requires abstraction and brings the matter that is considered essential into focus.

Precision and logical consistency are not equivalent to truth.

However, all those strengths also carry a risk. Precision and logical consistency are not equivalent to truth. Academics trained in mathematics frequently feel the beauty or elegance of an argument. However, what may be a quality factor in the realm of pure mathematics has no relevance to statements pertaining to the social world, which often seems chaotic.

Transparency and plausibility of arguments are relevant only to people trained in mathematics. Since the majority of other social sciences and humanities scholars are not trained in mathematics, they find it impossible to comprehend economic theories. At the same time, economists consider long texts and theories that are written out in words exhausting. Thus, exchange between the disciplines barely takes place anymore, even though it is indispensable in order to gain a comprehensive understanding of socially relevant issues.

The traditional mathematical toolset makes it difficult, for example, to analyse the distribution of income and wealth. Consequently, economists have long neglected this socially highly relevant issue. The same applies to the distribution and impact of power. Abstraction results in widespread optimism among economists: it is no problem at all to imagine sustainable, exponential growth in mathematical models. Imagining permanent exponential growth, however, is hardly feasible in the real world with its ecological limits.
Our language shapes the way we see the world. It determines what we consider true and what false – and what we consider feasible. We, in turn, shape the world through the manner in which we describe it. Mathematics is indeed useful in economics. However, it is necessary to regard it critically.

Modern economists would be well advised to recollect this approach.

Alfred Marshall, one of the founding fathers of modern economics, called for a prudent and measured approach to mathematics at the beginning of the 20th century. As far as he was concerned, a good mathematical theory was unlikely to be good economics. He recommended: “Use mathematics as a shorthand language, rather than an engine of inquiry. Translate the results into natural language. Illustrate the argument by examples that are important in real life. Burn the mathematics.” Modern economists would be well advised to recollect this approach.